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0099-2399/97/2302-0077503.00/0
JOURNAL OF ENDODONT{CS
Copyright 1997 by The American Association of Endodontists
S C I E N T IF IC A R T IC L E S
Pr in ted in U S A
VOL. 23 No. 2 FI~BRUARY1997
Cyc l i c F a t i g u e T es t i n g o f N i cke l T i tan i u m
E n d o d o n t i c I n s t r u m e n t s
J o h n P . P r u e tt D D S D a v i d J . C l e m e n t D D S a n d D a v i d L . C a r n e s J r. P h D
Cyc l i c fa t i gue o f n i cke l - t i tan ium, eng ine -d r i ven in -
s t r u m e n t s w a s s t u d i e d b y d e t e r m i n in g t h e e f f e c t o f
ca n a l cu r va tu r e a n d o p e r a t i n g sp e e d o n t h e b r e a k -
a g e o f L i g h t sp e e d i n s t r u me n ts . A n e w me th o d o f
ca n a l cu r va tu r e e va l u a t io n t h a t a d d r e ss e d b o th a n -
g l e a n d a b r u p tn e ss o f cu r va tu r e wa s i n t r o d u ce d .
Ca n a l cu r va tu r e wa s s i mu l a te d b y co n s t r u c t i n g s i x
cu r ve d s ta i n l e ss - s te e l g u i d e t u b e s w i t h a n g l e s o f
cu rva tu re o f 30 , 45 , o r 60 degrees , and rad i i o f
cu r va tu r e o f 2 o r 5 mm. S i ze 3 0 a n d 4 0 L i g h t -
s p e e d i n s t r u m e n t s w e r e p l a c e d t h ro u g h t h e g u i d e
tu b e s a n d t h e h e a d s se cu r e d i n t h e co l l e t o f a
Ma g t r o l Dyn a mo me te r . A s i mu l a te d o p e r a t i n g l o a d
o f 1 0 g - cm wa s a p p l i e d . I n s t r u me n ts we r e a b l e t o
r o ta te f r e e l y i n t h e t e s t a p p a r a tu s a t sp e e d s o f 7 5 0 ,
1 3 0 0 , o r 2 0 0 0 r p m u n t i l se p a r a t i o n o ccu r r e d . Cy -
c l e s t o f a i l u r e we r e d e te r m i n e d . Cyc l e s t o f a i l u r e
we r e n o t a f fe c te d b y r p m. I n s t r u m e n ts d i d n o t se p -
a r a te a t t h e h e a d , b u t r a th e r a t t h e p o i n t o f ma x i -
mu m f l e xu r e o f t h e sh a f t , co r r e sp o n d i n g t o t h e
m i d p o i n t o f cu r va tu r e w i t h i n t h e g u i d e t u b e . Th e
i n s t r u me n ts w i t h l a r g e r d i a me te r sh a f ts , 4 0 , f a il e d
a f t e r s i g n i fi ca n t ly f e w e r cyc l e s t h a n d i d 3 0 i n s t r u -
me n ts u n d e r i d e n t i ca l t e s t co n d i t i o n s . Mu l t i va r i -
a b l e a n a l ys i s o f va r i a n ce i n d i ca te d t h a t cyc l e s t o
fa il u re s i g n i f ica n t l y d e c r e a se d a s t h e r a d i u s o f cu r -
v a t ur e d e c r e a s e d fr o m 5 m m t o 2 m m a n d a s t h e
a n g l e o f cu r va tu r e i n c r e a se d g r e a te r t h a n 3 0 d e -
g rees (p < 0 .05 , power = 0 .9 ) . Scann ing e lec t ron
m i c r o sco p i c e va l u a t i o n r e ve a l e d d u c t i l e f r a c tu r e
a s t h e f a t i g u e f a i lu r e m o d e . Th e se r e s u l t s i n d i ca te
tha t , fo r n i cke l - t i tan ium, eng ine -d r i ven ro ta ry i n -
s t r u me n ts , t h e r a d i u s o f cu r va tu r e , a n g l e o f cu r va -
tu r e , a n d i n s t r u me n t s i ze a r e mo r e i mp o r ta n t t h a n
o p e r a t i n g sp e e d f o r p r e d i c t i n g se p a r a t i o n . Th i s
s t u d y s u p p o r t s e n g i n e e ri n g c o n c e p t s o f c y c l ic f a -
t i g u e f a il u re a n d su g g e s t s t h a t s t a n d a r d i ze d f a -
t i g u e t e s t s o f n i cke l - t i t a n i u m r o ta r y i n s t r u me n ts
sh o u l d i n c l u d e d yn a m i c o p e r a t i o n i n a f l e xe d s ta te .
Th e r e su l t s a l so su g g e s t th a t t h e e f f e c t o f t h e r a -
d i u s o f cu r va tu r e a s a n i n d e p e n d e n t va r i a b l e
sh o u l d b e co n s i d e r e d wh e n e va l u a t i n g s tu d i e s o f
r o o t ca n a l i n s t r u me n ta t i o n .
77
Instrument separation is a serious concern in endodontic s. Because
stainless-steel instruments usually deform before they separate,
dentists can inspect them for visible signs of instrument deforma-
tion. A deformed instrument usually shows severe bending or
unwinding of the flutes, indicating hat the elastic limit of the metal
has been exceeded and that the instrumen t should be discarded.
Nickel-titanium Ni-Ti) endodontic instruments were intro-
duced to facilitate instrumentation of curved canals. Ni-Ti instru-
ments are superelastic and will flex far more than stainless-steel
instruments before exceeding their elastic limit 1, 2). This flexi-
bility is an important property that allows preparation of curved
canals while minimizing transportation 3). Despite this increased
flexibility, separation is still a concern with Ni-Ti instruments, and
they have been reported to undergo unexpected fracture 4). Sep-
aration can occur without any visible signs of previous permanent
deformation, apparently within the elastic limit of the instrument.
Visible inspection, therefore, is not a reliable method for evalua-
tion of used Ni-Ti instruments.
The American Dental Association ADA) Specification No. 28
5) stipulates the design requirements, testing procedures, and
physical properties for endodontic instruments. Tests detailed in
ADA Specification No. 28 are conducted in a static mode. Instru-
ments are fixed at the tip and are twisted until failure to determine
instrumen t resistance to fracture under torsional loading. Angular
deflection is used to detertnine stiffness when instruments are bent
to predetermined angles of 30, 45, and 90 degrees. Tests described
in ADA Specification No. 28 are appropriate for establishing
mini mum strength requirements of Ni-Ti hand instruments placed
under a static load I, 2, 6, 7), but ADA Specification No. 28 is not
an appropriate test of the dynamic characteristics of engine -driven
rotary instruments. All Ni-Ti, engine-dr iven otary systems require
that the ins trument be activated at a predetermined rpm before
inser tion into the canal. Therefore, to test rotary inst ruments, the
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7 8 P r u e t t e t a l
t i p s h o u l d n o t b e s t a t i c a l l y l o c k e d , b u t a l l o w e d t o r o t a t e f r e e l y .
B e c a u s e A D A S p e c i f i c a t i o n N o . 2 8 d o e s n o t c o n s i d e r c a n a l g e -
o m e t r y , i t a l s o d o e s n o t c o n s i d e r f a t i g u e a n d b r e a k a g e o f r o t a ry
i n s t r u m e n t s o p e r a t e d i n f l e x e d c o n d i t i o n s w h i l e p r e p a r i n g c u r v e d
c a n a l s. T h e p h e n o m e n o n o f r e p e a t e d c y c l i c m e t a l fa t i g u e c au s e d
b y c a n a l c u r v a t u r e s m a y b e t h e m o s t i m p o r t a n t f a c t o r in i n s t r u m e n t
separa t ion (2, 8) .
N i - T i i n s t r u m e n t s e x h i b i t s u p e r e l a s t i c b e h a v i o r a n d r e m a i n
w i t h i n t h e i r e l a s ti c l i m i t i n s i tu a t i o n s t h a t w o u l d c a u s e p e r m a n e n t
p la s t i c de form a t ion in s t a in le s s - s te e l ins t rum e nts (1 , 2 ) . Me ta l
f a t i g u e ( c y c l i c f a t i g u e ) l e a d i n g t o f r a c t u r e a n d s e p a r a t io n c a n o c c u r
b e l o w t h e e l a s t i c l i m i t o f t h e i n s t r u m e n t ( w i t h o u t p e r m a n e n t d e -
f o r m a t i o n ) t h r o u g h k n o w n m e c h a n i s m s c a l l e d s l i p b a n d s ( 9 ) . S u c h
f a t i g u e m e c h a n i s m s o c c u r m i c r o s c o p i c a l l y a n d a r e n o t v i s i b l e t o
t h e e y e . C y c l i c f a t i g u e i s ca u s e d b y r e p e a t e d t e n s i l e - c o m p r e s s i v e
s t r e s s . R o t a t i o n s u b j e c t s a n e n d o d o n t i c i n s t r u m e n t t o b o t h t e n s i l e
a n d c o m p r e s s i v e s t r e s s i n t h e a r e a o f t h e c u r v e . I n s t r u m e n t s p l a c e d
i n c u r v e d c a n a l s d e f o r m , c r e a t i n g s t r e s s w i t h i n t h e i n s tr u m e n t . H a l f
o f t h e i n s t r u m e n t s h a f t o n t h e o u t s i d e o f t h e c u r v e i s i n t e n s i o n , a n d
t h a t h a l f o f t h e i n s t r u m e n t s h a f t o n t h e i n s i d e o f t h e c u r v e i s i n
c o m p r e s s i o n . E a c h r o t a t i o n w i t h i n a c u r v e d c a n a l c a u s e s a n i n s tr u -
m e n t t o u n d e r g o o n e c o m p l e t e t e n s i o n - c o m p r e s s i o n s t r e s s c y c l e .
T h i s i s t h e m o s t d e s t r u c t i v e f o r m o f c y c l i c l o a d i n g ( 9 ) .
A l t h o u g h s o m e d y n a m i c t e s t i n g h a s b e e n p e r f o r m e d o n N i - T i
a n d s t a i n l e s s - s t e e l e n d o d o n t i c i n s t r u m e n t s ( 2 , 8 , 1 0 - 1 3 ) , f a t i g u e
t e s t i n g r e m a i n s u n d e v e l o p e d a s a n e n d o d o n t i c i n s t r u m e n t t e s t i n g
m e t h o d o l o g y ( 2 , 1 0 , 1 1 ) . S t r es s l e v e l s d u r i n g c y c l i c l o a d i n g a r e
g e n e r a l l y d e p e n d e n t o n t h e a c t u a l s h a p e o f t h e c u r v a t u r e a n d t h e
a ppl ie d loa ds . Thi s s t r e s s i s gre a te s t in the a re a of c urva tu re (14) .
More se ve re be nds c re a te gre a te r s t r e s s (14) ; a nd l a rge r , s t i f f e r
i n s t r u m e n t s w i l l e x p e r i e n c e g r e a t e r s t r e s s t h a n s m a l l e r i n s t ru m e n t s
w h e n c o n f i n e d t o t h e s a m e c u r v e d c a n a l s h a p e .
T h e p u r p o s e o f t h i s s t u d y w a s 2 - f o l d ; f i r s t t o i n t r o d u c e a n e w
m e t h o d o f d e t e r m i n i n g c a n a l c u rv a t u r e . A n e w m e t h o d w a s n e c -
e s s a r y b e c a u s e c a n a l c u r v a t u r e h a d t o b e d e s c r i b e d i n p a r a m e t e r s
k n o w n t o d e t e r m i n e i n s t r u m e n t s t re s s a n d t h e r e f o r e a f f e c t i n st r u -
m e n t f a t i g u e l i f e . S e c o n d , c y c l i c f a t i g u e w a s e x a m i n e d i n a c o m -
m e r c i a l l y a v a i l a b l e N i - T i i n s t r u m e n t s y s t e m . T h e s t u d y e x a m i n e d
t h e e f f e c t o f i n s t r u m e n t o p e r a t i n g r p m , s h a f t d i a m e t e r , a n d c a n a l
c u r v a t u r e ( i n c l u d i n g a n g l e o f c u r v a t u r e a n d r a d i u s o f cu r v a t u r e ) o n
t h e f a t i g u e l i f e a n d r e s u l t i n g s e p a r a t i o n o f N i - T i a l l o y e n d o d o n t i c
ins t rum e nts .
M A T E R ~ L S A N D M E T H O D S
T h i s s t u d y r e q u i r e d d e f i n i n g t h e p a r a m e t e r s o f c a n a l cu r v a t u r e
i n a m o r e e x a c t m a n n e r t h a n g e n e r a l l y u s e d i n e n d o d o n t i c r e s e a rc h .
C a n a l c u r v a t u r e i s u s u a l l y d e p i c t e d b y a s i n g l e p a r a m e t e r , a n
a r b i tr a r y a n g l e m e a s u r e d i n d e g r e e s a s d e s c r i b e d b y S c h n e i d e r ( 1 5 )
( F i g . 1 ) . T o d e t e r m i n e t h e d e g r e e o f r o o t c u r v a t u r e , h e s c r i b e d a
l i n e p a r a l le l t o t h e l o n g a x i s o f t h e c a n a l. A s e c o n d l i n e w a s d r a w n
f r o m t h e a p i c a l f o r a m e n t o i n t e r s e c t w i t h t h e f i r st l i n e a t t h e p o i n t
w h e r e i n t h e c a n a l b e g a n t o l e a v e t h e l o n g a x i s o f t h e c a n a l. T h e
a c u t e a n g l e f o r m e d ( a ) w a s d e f i n e d a s t h e d e g r e e o f ro o t c u r v a t u r e .
T h e s h a p e o f a n y r o o t c a n a l c u r v a t u r e i s m o r e a c c u r a t e l y d e -
s c r i b e d u s in g t w o p a r a m e t e r s : a n g l e o f c u r v a t u r e ( a ) a n d r a d i u s o f
c u r v a t u r e ( r ) ( F i g . 2 ) . T o d e t e r m i n e t h e s e p a r a m e t e r s , a s t r a i g h t l i n e
i s d r a w n a l o n g t h e l o n g a x i s o f t h e c o r o n a l p o r t i o n o f t h e ca n a l . A
s e c o n d l i n e i s d r a w n a l o n g t h e l o n g a x i s o f t h e a p i c a l p o r t i o n o f th e
c a n a l . T h e r e i s a p o i n t o n e a c h o f t h e s e l i n e s a t w h i c h t h e c a n a l
d e v i a t e s t o b e g i n ( p o i n t a ) o r e n d ( p o i n t b ) t h e c a n a l c u r v a t u r e . T h e
J o u r n a l o f E n d o d o n U c s
3
B
F IG 1 . Deg r ee o f r oo t c ana l c u r va t u r e . T he m e t hod des c r i bed by
S c hne i de r f o r de t e r m i n i ng c ana l c u r v a t u r e us es on l y one pa r am e t e r
t o de f i ne t he ang l e . T t =, t wo s i m u l a t ed t ee t h dem ons t r a t e h ow a
d i f fe rence i n abruptne~ , , o f the curve rad ius o f curvature) w i l l vary
t h e d e g r e e o f c u r v a t u r e a s m e a s u r e d b y t h i s m e t h o d . A h a s a n a n g l e
o f 43 deg r ee s and B has an ang l e o f 52 deg r ees , ev en thou gh b o t h
a n g l e s m e a s u r e d a c c o r d i n g t o o u r m e t h o d e q u a l e d 6 0 d e g r e e s .
L o c a t i o n o f t h e c u r v e a l o n g t h e c a n a l w i ll a l s o c h a n g e t h e m e a s u r e d
ang l e .
c u r v e d p o r t i o n o f t h e c a n a l i s r e p r e s e n t e d b y a c i r c l e w i t h t a n g e n t s
a t p o i n t s a a n d b . T h e a n g l e o f c u r v a t u r e i s t h e n u m b e r o f d e g r e e s
o n t h e a r c o f t h e c i r c le b e t w e e n p o i n t s a a n d b . A n g l e o f c u r v a t u r e
c a n a l s o b e d e f i n e d b y t h e a n g l e f o r m e d ( c ~ 1 a nd c ~2) by pe rp e n-
d i c u l a r l i n e s d r a w n f r o m t h e p o i n t s o f d e v i a t i o n ( a a n d b ) t h a t
i n t e r s e c t a t t h e c e n t e r o f t h e c i r c l e . T h e l e n g t h o f t h e s e l i n e s i s t h e
r a d i u s o f t h e c i r c l e a n d d e f i n e s t h e r a d i u s o f t h e c a n a l c u r v a t u r e .
T h e r a d i u s o f c u r v a t u r e ( r I a n d r 2 ) i s t h e l e n g t h o f t h e r a d i u s o f t h e
c i r c l e m e a s u r e d i n m i l l i m e t e r s . T h e r a d i u s o f c u r v a t u r e r e p r e s e n t s
h o w a b r u p t l y o r s e v e r e l y a s p e c i fi c a n g l e o f c u r v a t u r e o c c u r s a s t h e
c a n a l d e v i a t e s f r o m a s t r a i g h t l i n e . T h e s m a l l e r t h e r a d i u s o f
c u r v a t u r e , t h e m o r e a b r u p t t h e c a n a l d e v i a t i o n . T h e p a r a m e t e r s o f
a n g l e o f c u r v a t u r e a n d r a d i u s o f c u r v a t u r e a r e i n d e p e n d e n t o f e a c h
o t h e r . C a n a l s c a n h a v e t h e s a m e a n g l e o f c u r v a t u r e w h i l e h a v i n g
d i f f e r e n t r a d i i o f cu r v a t u r e , r e s u l t in g i n m o r e a b r u p t c u r v e s .
B e c a u s e c o n t r o l l e d c y c l i c f a t i g u e s t u d i e s o n N i - T i , e n g i n e -
d r i v e n e n d o d o n t i c i n s t r u m e n t s h a d n o t p r e v i o u s l y b e e n p e r f o r m e d ,
p i l o t s t u d ie s w e r e r e q u i r e d t o d e v e l o p a t e s t ap p a r a t u s a n d s p e c i f y
t h e t e st p a r a m e t e r s . T h e p a r a m e t e r s o f r a d i u s o f c u r v a t u r e a n d
a n g l e o f c u r v a tu r e n e e d e d t o b e d e f i n e d n a r r o w l y e n o u g h t o a l l o w
a c c u r a t e d a t a c o l l e c t i o n . E x t r a c t e d t e e t h w i t h s e v e r e r o o t c u r v a -
t u r e s s u g g e s t i n g p o s s i b l e h i g h - s t r e s s c o n d i t i o n s l e a d i n g t o i n s t r u -
m e n t s e p a r a t i o n w e r e r a d i o g r a p h e d . R a d i o g r a p h s w e r e a l s o m a d e
o f t e e th t r e a t e d c l i n i c a l l y in w h i c h s e p a r a t i o n o f N i - T i L i g h t s p e e d
i n s t r u m e n t s h a d o c c u r r e d . T h e r a d i u s o f c u r v a t u r e o f t h e c a n a l s i n
t h e s e t e e th w a s d e t e r m i n e d b y u s i n g a c i r c l e g a u g e a l i g n e d o v e r t h e
i m a g e o f t h e c a n a l p r o f i l e . A d d i t i o n a l l y , s i z e 3 0 L i g h t s p e e d
i n s t r u m e n t s w e r e o p e r a t e d t h r o u g h b e n t n e e d l e s s i m u l a t i n g i n -
c r e a s i n g c a n a l c u r v a t u r e s . I n s t r u m e n t s t e s t e d i n c a n a l s h a v i n g a
5 - m m r a d iu s o f c u r v a tu r e w i t h a n a n g l e o f c u r v a t u re o f 3 0 d e g r e e s
s e p a r a t e d a s a r e s u l t o f c y c l i c f a t ig u e . S t r e s s l e v e l s i n d u c e d b y
l e s s e r c u r v a t u r e s d i d n o t r e s u l t i n in s t r u m e n t s e p a r a t i o n ( o c c u r r i n g
i n o v e r 3 0 m i n a t a s p e e d o f 2 0 0 0 r p m ) w i t h i n t h e t i m e f r a m e f o r
t h e t e s t a p p a ra t u s o r d a t a c o l l e c t io n . T h u s , a n g l e s o f c u r v a t u r e o f
3 0 , 4 5 , a n d 6 0 d e g r e e s w e r e c h o s e n f o r e v a l u a t i o n a t r a d i i o f
c u r v a t u r e o f 2 a n d 5 m m .
T o s i m u l a t e i n s t r u m e n t a t i o n c o n d i t i o n s d u r i n g u s e , a c l i n i c a l l y
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V o l. 23 N o . 2 F eb ru ary 1997
o~ = 60 o~z =6 0
r = rnrn
A B
F IG 2 . Rad i us o f c u r v a t u r e and an g l e o f c u r v a t u r e . New m e t ho d o f
des c r i b i ng c ana l geom e t r y us ing t wo pa r am e t e r s . Rad i us o f c u r v a -
t u r e ( r) and ang l e o f c u r v a t u r e ( e ) a r e de t e r m i ned on t he s am e t ee t h
as i n F ig . 1 . T hes e t ee t h ac c u r a t e l y dep i c t t he gu i de t ubes us ed i n
t h i s s t udy t ha t had a 6 0 - deg r ee ang l e ( (~ 1 = ( x2 ). A ng l e o f c u r v a t u r e
(c~) i s de t e r m i ne d b y t he ang l e f o r m ed by t h e l ines t ha t i n t e r s ec t a t
t he c i r c l e s c en t e r . T hes e t wo l ines a r e pe r pe nd i c u l a r t o t he l ines
d r awn a l ong t he l ong ax es o f t he c o r ona l and ap i c a l po r t ions o f t he
r oo t c ana l s pac e . P o i n t s a and b a r e t he po i n t s whe r e i n t he c ana l
dev i a t es f rom t he s t r a i gh t l ines and e i t he r beg i n o r end t he c u r v ed
po r t i on o f t h e r oo t c ana l s pac e . A ng l e ( (~ ) is t ak en t o be t he ang l e
f o r m ed by t he a r c in deg r ees be t w een po i n t s a and b . T he
rc
l ies
on a c i r c le w hos e s i z e is s pec i f i ed b y i t s r ad i us, an d t he c i r c le s
r ad i us is t ak en t o be t he r ad i us o f c u r v a t u r e o f t he c ana l i n t ha t l oc a l
area. The c i r c l e s rad ius i s the rad ius ( r l and r2) o f the cu rved por t i on
o f t he r oo t c ana l s pac e and de f i nes how ab r up t l y t he c ana l c u r v es .
T he c an a l geom e t r y o f t hes e t wo t ee t h d i f fe r s on l y i n the r ad i us o f
curvature ( r~ and
r 2 ,
wher eas t he ang l e o f c u r v a t u r e ( ( x1 and (x2)
equa l s 60 deg r ees . A r ep r es en t s a s weep i ng c ana l c u r v a t u r e hav i ng
a 5 - m m r ad i us o f c u r v a t u r e ( r l) . B r ep r es en t s an ab r up t c ana l c u r-
vatu re hav ing a 2-m m rad ius o f curv ature ( r2) . C l i n i ca l ly , the rad ius o f
c u r v a t u re a n d a n g l e o f c u r v a tu r e o f a n y r o o t c a n a l s p a c e c o u l d b e
m eas u r ed us i ng t h is t ec hn i que w i t h t he a i d o f a c i r c le gauge .
a p p l i c a b l e h e a d t o r q u e l o a d w a s d e t e r m i n e d . D a t a w e r e o b t a i n e d
b y m e a s u r i n g t h e r e s u l t a n t t o r q u e w h e n h i g h l y c a l c i f i e d c an a l s i n
l o w e r c e n t r a l i n c is o r s w e r e i n s t r u m e n t e d w h i l e m o u n t e d i n a d y -
n a m o m e t e r . C a n a l p r e p a r a t i o n w i t h s u c c e s s i v e l y l a r g e r L i g h t s p e e d
i n s t r u m e n t s w a s p e r f o r m e d . W h e n s m a l l i n s t r u m e n t s d i d n o t a c -
t i v e l y e n g a g e a n d c u t t h e d e n t in w a l l s d u r i n g t h e p r e p a r a t i o n o f
l o w e r c e n t r a l i n c i s o r s , n o p e r c e p t i b l e t o r q u e v a l u e s c o u l d b e r e -
p e a t a b l y r e c o r d e d . W h e n a c t i v e d e n t i n c u t t i n g o c c u r r e d , r e c o r d e d
t o r q u e v a l u e s r a n g e d f r o m 6 t o 1 4 g - c m . T h e r e f o r e , a p r e se t t o r q u e
o f 1 0 g - c m w a s a p p l i e d t o t h e t e s t i n s t ru m e n t s d u r i n g a l l o f t h e t e s t
c o n d i t i o n s .
S i z e 3 0 a n d 4 0 L i g h t s p e e d i n s t r u m e n t s ( L i g h t s p e e d T e c h n o l -
o g i e s , I n c . , S a n A n t o n i o , T X ) w e r e e v a l u a t e d . L i g h t s p e e d i n s t r u -
m e n t s w e r e c h o s e n b e c a u s e t h e i r n o n c u t t i n g s h a f t s o f f e r t h e a d -
v a n t a g e s o f p r e d i c t a b l e s h a f t d i a m e t e r s . T h i s a l s o e l i m i n a t e d t h e
v a r i a b l e s o f i n s t r u m e n t t a p e r a n d f l u t e d e s i g n o n m e t a l f a t i g u e a n d
b r e a k a g e . S i z e 4 0 w a s s e l e c t e d b e c a u s e i t i s t h e m i n i m u m m a s t e r
a p i c a l s i z e a d v o c a t e d f o r th e L i g h t s p e e d t e c h n i q u e . S i z e 3 0 w a s
s e l e c t e d b e c a u s e i t is c o m p a r a t i v e l y s m a l l e r i n s i z e a n d h a s a h e a d
d e s i g n t h a t i s n e a r l y p a r a l l e l . I n a d d i t i o n , L i g h t s p e e d i n s t r u m e n t s
w e r e c h o s e n b e c a u s e t h e i r u s e h a s b e e n a d v o c a t e d o v e r a w i d e
r a n g e o f o p e r a t i n g s p e e d s . T e n i n s t r u m e n t s o f e a c h s i z e w e r e t e s te d
i n e a c h o f t h e s i x d i f f e r e n t e x p e r i m e n t a l c a n a l s h a p e s ( 3 a n g l e s c ~
e a c h o f 2 r a d i i r ) at t h r ee d i f f e r e n t s p e e d s ( 7 5 0 , 1 3 0 0 , a n d 2 0 0 0
r p m ) . T h i s p r o d u c e d 1 8 t e s t g r o u p s f o r e a c h i n s t r u m e n t s i z e . E a c h
i n s t r u m e n t w a s o p e r a t e d t o f a i l u r e .
C yc l i c F a t i g u e o f N i - T i R o t a ry I n s t ru m e n t s 79
Ni-Ti L ightspeed Inst rument
Tes t Suppor t B lock
Gu ide Tube
Ho lddown
.~ , . C lamp
Dynamomete r Co l l e t
L
I npu t sha f t t o dynamomete r , da ta aqu i s i t ion compu te r
F IG 3 . T es t appa r a t us . Cu t - awa y v i ew o f a L i gh t s peed i ns t r um e n t
i ns e r ted t h r ough t he l um en o f a s t a i n l es s -s t ee l gu i de t ube c l am ped
i n t he dy n am om et e r c o l le t . T he i ns t r um en t s hank bu t t s up aga i ns t
t he end o f t he gu i de t ube , ens u r i ng t ha t eac h i ns t r um en t was p l ac ed
t o t he s am e dep t h w i t h i n t he a r t i f i c i a l c ana l . T he dy nam om et e r
a l l owed f r ee r o t a t i on o f t he i ns t r um en t du r i ng t he c y c l ic f a t i gue t es t ,
y e t was c apab l e o f app l y i ng t o r s i ona l p r e l oad t o s i m u l a t e c l i n i c a l
u s e ,
B o t h r a d i u s o f c u r v a t u r e a n d a n g l e o f c u r v a t u r e w e r e u s e d t o
d e f i n e a c c u r a t e l y t h e c u r v a t u r e s o f a r t i f i c i a l c a n a l s u s e d i n t h i s
s t u d y . A r t i f i c i a l c a n a l s w e r e f a b r i c a t e d f r o m 1 8 - g a u g e , s t a i n l e s s -
s t e e l n e e d l e s h a v i n g a n i n t e r n a l d i a m e t e r o f 0 . 8 3 r a m . R e f e r e n c e
r a d i i w e r e m e a s u r e d t o t h e i n n e r a s p e c t o f t h e c u r v e o f t h e g u i d e
t u b e s . A 2 - m m r a d i u s r e p r e s e n t e d a n a b r u p t c u r v a t u r e ; a n d a 5 m m
r a d i u s r e p r e s e n t e d a s w e e p i n g c u r v a t u r e ( F i g . 2 ) , e a c h w i t h a n g l e s
o f c u r v a t u r e o f 3 0 , 4 5 , a n d 6 0 d e g r e e s . T h i s r e s u l t e d i n s i x a r t i f i c ia l
c a n a l s . O n e e n d o f t h e a r t if i c i a l c a n a l b u t t e d a g a i n s t t h e f l a t s h a n k
o f t h e i n s t ru m e n t , a n d t h e c e n t e r o f ra d i u s i n t h e c u r v e d s e g m e n t
o f t h e c a n a l w a s 7 m m f r o m t h e t i p o f t h e i n s t r u m e n t ( F i g . 3 ) . T h e
h e a d o f th e i n s t r u m e n t p r o t r u d e d - 2 m m f r o m t h e a r t if i c i a l c a n a l .
A t e s t s t a n d ( F i g . 3 ) w a s c o n s t r u c t e d t h a t a l i g n e d t h e i n n e r a s p e c t
o f t h e a r ti f i c ia l c a n a ls w i t h t h e c e n t e r l i n e o f t h e d y n a m o m e t e r a n d
h e l d t h e m s e c u r e l y i n p l a c e . I n s t r u m e n t s w e r e i n s e r t e d t h r o u g h t h e
c a n a l s , a n d t h e h e a d s w e r e c l a m p e d i n t h e c o l l e t o f t h e M a g t r o l
D y n a m o m e t e r ( M a g t r o l , I n c . , B u f f a l o , N Y ) . C l a m p e d i n s t r u m e n t s
c o u l d r o t a t e f r e e l y w i t h i n t h e t u b e a s s e m b l y . A n A s e p t i c o e l e c t r i c
h a n d p i e c e ( A s e p t i c o m o d e l A E U - 1 7 , A s e p t i c o , In c . , W o o d i n v i l l e ,
W A ) w a s a t t a c h e d t o t h e i n s t r u m e n t s h a n k . T h e e x p e r i m e n t a l
o p e r a t i n g s p e e d o f 7 5 0 , 1 3 0 0 , o r 2 0 0 0 r p m w a s a d j u s t e d u s i n g t h e
d y n a m o m e t e r r e a d o u t t h a t p r o v i d e d a m o r e a c c u r a t e r p m d e t e r m i -
n a t i o n t h a n d i d t h e r e a d o u t o n t h e A s e p t i c o c o n t r o l b o x . R o t a t i o n
a t t h e d e s i r e d s p e e d w a s a c h i e v e d b y a c t i v a t i n g t h e A s e p t i c o
e l e c t r i c h a n d p i e c e .
T h i s s t u d y u s e d i n s tr u m e n t a ti o n e q u i p m e n t s p e c i f i e d in A D A
S p e c i f i c a t i o n N o . 2 8 f o r t o r s i o n a l t e s t i n g : t h e M a g t r o l Dynamom
8/10/2019 cyclic fatigue of NiTi instruments
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80 Pruett et al.
eter. The dynamometer allows the torque applied to the instrument
to be preset and measured while the instrument rotates. All instru-
ments were operated with a head load of 10 g-cm torque. A
software program (Sunset Resources, Inc., San Antonio, TX) was
written for an IBM-compatible computer to permit data collection
while the inst rument was rotating. A n 18-rain time limit for data
collection was set as limited by the data collection program, but
instrument separation always occurred within 5 min of beginn ing
the test. Data collection from the dynamometer consisted of con-
tinuous torque, and rpm readouts were comprised of 10 averaged
readings/s. The time of instrument failure was determined when
the torque values suddenly dropped, indicating instrument separa-
tion. The number of cycles to failure was calculated from the rpm
data by multiplying the rpm by the time to failure. Data analyzed
were the number of cycles to fa ilure for each inst rument tested
under the specified angle of curvature, radius of curvature, rpm,
and instrumen t size conditions. Data were analyzed by analysis of
variance (ANOVA), with the Neuman-Kuels procedure serving as
the post-hoc test using a 95% confidence level.
Fractured inst rument fragments were collected by group. Rep-
resenta tive samples of the fracture surface from the various groups,
and sizes were examined under scanning electron microscopic
magnification with a JSM-840 scanning electron microscope
(Japanese Electronic and Optical Ltd., Japan). Another group of
instruments was partially cycled (75 to 80% to failure) using mean
cycles-to-failure data from the matching experimental groups.
These instruments were then mounted in both unflexed and flexed
positions with the area of interest visible in side view, and exam-
ined under scanning electron microscopy (SEM). For comparison,
new same-sized instruments were mounted in the same manner and
examined under SEM.
RESULTS
Operating rpm
Multivariable ANOVA indicated that operating rpm was not a
significant factor affecting cycles to failure (p < 0.10 for size 30;
p < 0.06 for size 40) (Fig. 4). No difference in cycles to failure
was recorded between the 750, 1300, and 2000 rpm groups within
the two instrument sizes. This was further verifi ed by one-way
ANOVA, wherein only 2 of the possible 36 groups in the size 30
and 40 instrument groups had cycles to failure that varied when
rpm was the only independent variable evaluated.
Instrument Shaft Diameter
Shaft diameter had a signif icant effect on cycles to failure (p .
o
1000
900
800
700
600
500
400
300
200
100
0
5ram Radius 2ram
Radius
SIZE 40
30 degrees ~ 45 degreee ~ 60
degrees
FIG 6. E ffect of angle of curvature. Angle subgro ups are arranged
according to radius of curvature for size 30 (A) and 40 (B) instru-
ments. Forty-five degree or 60-degree angles in both instrument
size groups had significantly fewer cycles to failure than the 30-
degree angle groups (*). The size 40, 2-mm radius subgroup varied
from this pattern, w ith all angles having significantly different cycles
to failure (** and ***).
meri t s ize exis t , which s igni f icant ly reduce ins t rument cycl ic fa-
tigue life.
There i s a c lear need for the developmen t of a tes t protocol for
the cycl ic fa t igue of Ni-Ti , engine-dr iven rotary ins t ruments .
Brantle y et al . 10) and Luebke et al. 11), in studies on stainless-
s tee l rotary ins t ruments , have a lso advocated the dev elopmen t of a
cycl ic fa t igue tes t protocol that s imulates c l in ica l condi t ions of
ins t rument use . Serene e t a l . 2) publ ished a shor t volume on Ni-Ti
instruments, including results from a preliminary study on rotation
to breakage cycl ic fa t igue) of hand ins t ruments . A s igni f icant
di f ference was found between c onvent ional s ta inless-s tee l f i les and
all Ni-Ti fi le groups. It was also noted that in rotation-to-breakage
studies of Ni-Ti f i les that a l lowed f ree t ip rota t ion, the range of
resul ts wi thin each same-s ize group was large and unpredic table .
That pre l iminary informat ion on rota t ion- to-breakage of hand in-
struments stated that the instruments were rotated in a 90-degree
metal tube until they broke. Defining the test parameters in such a
l imi ted manner , w i thout s t r ic t ly control l ing the var iables of curv e
geometry, may expla in the var iabi li ty in rota t ion- to-breakage cy-
8/10/2019 cyclic fatigue of NiTi instruments
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82 Pruett et al Journal of Endodont ics
FIG 7. Location of separation. Ran domly selected size #40 Light-
speed instruments that w ere cycled to failure. All instruments tested
showed the same pattern of separation, with fractures occurring
within the guide tube at the midpoint of the curved segment.
D
FIG 8. Partially separated instruments. Partially separated instru-
ments ap pear normal to the eye (A), and under SEM evaluation in an
unflexed state at x150 original magnification (B).
A r r o w s
indicate
the location of the fracture in-the unflexed instrument, which is
closed and not apparent. Upon mounting the instrume nt shaft in a
flexed (stressed) position (C), incomple te fractures be came appar-
ent under SEM examination at x150 original magnification (D).
A r r o w s
indicate the same site of exam ination of the instrument shaft,
which corre lated to the midpoint of the curved segment of the guide
tube.
cles to fa i lure) resul ts and the conclus ion drawn concerning N i-Ti
ins t ruments . Parameters including radius of curvature , angle of
curvature, instrument size, and the point of maximal instrument
f lexure were a l l found to have a s igni f icant ef fec t on the number of
cycles to fa i lure and locat ion of breakage in our s tudy. Al l of these
factors should be considered when developing a tes t protocol for
the examinat ion of cycl ic fa t igue .
Mathemat ics and engineer ing pr inciples 14) suggest tha t a
system is needed that describes canal geometry in terms that
consistently describe the state of stress and cyclic fatigue on a
f lexed ins t rument shaf t . The independent var iables that descr ibe
canal shape are radius of curvature and angle of curvature . The
usual method of measur ing canal curvature publ ished by Schneider
15) in 1971 provides a means of estimating canal shape using a
single parameter: an estimated arbitrary angle Fig. 1). This
method does not consider radius of curvature as a measurable
aspect of canal geometry. Using only one parameter to descr ibe
canal shape does not d i f ferentia te the canal shape by abruptness o r
radius of curvature. Two canals measured at the same angle in
FIG 9. S tages of instrument fracture. A show s the fracture surface of
a size #30 instrume nt at 300 original magnification. The b o x e d a r ea
is enlarged in B having a x190 0 original magnification. The
aster isk
indicates the area of crack init iation on the periphery. Crack p rop-
agation is seen in B as striations marked by the ar rows Each
striation represents a jump in the fracture surface that occurred
under tension in that area during rotation. Ultimate ductile fracture is
seen in the central area of A, characterized by the presence of
microvoid formations and dimpling.
degrees by the S chneider method could have ve ry di f ferent radi i or
abruptness of curvatures, thus having a very different impact on the
di f f iculty of canal ins t rumentat ion and ins t rument fa t igue .
The more exact method of determining canal curvature and
geometry descr ibed in th is s tudy considers the radius of curvature
r) and the angle of curvature a) separately Fig. 2). Thes e are
terms that mathema tically specify the shape factors of a curved
root canal sys tem. The radius of curvature in mi l l imeters) i s the
radius of a circle that coincides with the path taken by the canal in
the area of the most abrupt curvature. A more abrupt curve cor-
responds to a smal ler radius of curvature . The angle of curvature
is the degrees arc formed between the points of devia t ion on the
ci rc le, or the angle formed between the perpendicular l ines drawn
from the tangents in tersecting at the center of the circle Fig. 2).
The angle of curvature i s independent of the radius . Thus , two
canals wi th the same degree of curvature can have radical ly di f -
ferent radii . Pilot studies were required to define systematically the
range of parameters for th is s tudy on cycl ic fa t igue . The radi i of
curvature and angles of curvature chosen could be considered so me
of the more s igni f icant tha t are encountered in c l in ica l pract ice .
When the s imulated canals in th is s tudy were measured us ing the
Schneider method, the 2-mm radius , 30- , 45- , and 60-degree angle
groups measured 26, 40, and 52 degrees , respect ively . The 5-mm
radius, 30-, 45-, and 60-degree angle groups measured 24, 35, and
43 degrees , respect ively . Authors have c i ted average canal curva-
8/10/2019 cyclic fatigue of NiTi instruments
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V o l . 23 N o . 2 F eb ru ary 1997
t u r e s f o r m a n d i b u l a r m o l a r s m e a s u r e d u s i n g t h e S c h n e i d e r m e t h o d
b e t w e e n 2 0 t o 3 0 d e g r e e s , w i t h r a n g e s b e t w e e n 6 t o 4 8 e g r e e s
( 1 6 ) . O u r 3 0 - d e g r e e a n g l e g r o u p s a r e w e l l w i t h i n t h e a v e r a g e s o f
c a n a l m e a s u r e m e n t t o b e c l i n i c a l l y r e l e v a n t , w h e r e a s t h e a n g l e s
l a r g e r t h a n 3 0 d e g r e e s w o u l d b e e x p e c t e d t o b e e n c o u n t e r e d l e s s
f r e q u e n t l y .
O f t h e t w o c a n a l - s h a p e p a r a m e t e r s , a n g l e a n d r a d i u s o f c u r v a -
t u r e , r a d i u s o f c u r v a t u r e w a s t h e m o s t s i g n i f i c a n t f a c t o r o f c a n a l
s h a p e a f f e c t i n g t h e n u m b e r o f c y c l e s t o f a i l u r e o f N i - T i , e n g i n e -
d r i v e n r o t a r y i n s t r u m e n t s . C o n s i s t e n t l y , a d e c r e a s e i n t h e ra d i u s o f
c u r v a t u r e f r o m 5 m m t o 2 m m r a d i u s r e s u l t e d i n a s i g n i f i c a n t
d e c r e a s e i n t h e n u m b e r o f c y c l e s t o fa i l u r e ( F ig . 6 ) . E x p l a n a t i o n o f
t h e e f f e c t o f r a d i u s i s c o m p l e x , b u t c a n b e g r o s s l y s i m p l i f i e d b y
s t a ti n g t h a t s t r e ss o n t h e i n s t r u m e n t i s i n v e r s e l y p r o p o r t i o n a l t o t h e
r a d i u s o f c u r v a tu r e . T h e r e f o r e , a s t h e r a d i u s o f c u r v a t u r e d e c r e a s e s ,
i n s t r u m e n t s t r e s s a n d s t r a i n i n c r e a s e s , a n d t h e f a t i g u e l i f e d e -
c r e a s es . T o o u r k n o w l e d g e , r a d i u s o f c u r v a t u r e h a s n o t b e e n
p r e v i o u s l y c o n s i d e r e d a s a s e p a r a t e i n d e p e n d e n t v a r i a b l e i n a n y
i n s t r u m e n t a t i o n s t u d y .
C l i n i c a l l y , t h e s w e e p i n g c u r v a t u r e o f t h e 5 - m m r a d i u s g r o u p s ,
a l t h o u g h c h a l l e n g i n g , i s a m u c h l e s s d i f f i c u l t c a n a l c u r v a t u r e t o
m a n a g e t h a n t h e a b r u p t c u r v a t u r e r e p r e s e n t e d b y t h e 2 - m m r a d i u s
g r o u p s . A b r u p t c u r v a t u r e s p r e d o m i n a t e i n t h e a p i c a l t h i r d o f t h e
c a n a l o r i n d i l a c e r a t e d r o o ts . B o t h c o n d i t i o n s a r e a s s o c i a t e d w i t h a n
i n c r e a s e d i n c i d e n c e o f i n s t r u m e n t s e p a r a t i o n . D e g r e e o f r o o t c u r -
v a t u r e a n d i n s t r u m e n t s t i f f n e s s h a v e b e e n i m p l i c a t e d i n c a n a l
p r e p a r a t i o n e r r o r s , s u c h a s i n s t r u m e n t b r e a k a g e , l e d g i n g , b l o c k -
a g e s , z i p p i n g , a n d p e r f o r a ti o n . H o w e v e r , r a d i u s o f c u r v a t u r e w i t h
i t s r e s u l t an t i n c r e a s e d s t r e s s o n e n d o d o n t i c i n s t r u m e n t s m a y a l s o b e
a s i g n i f i c a n t f a c t o r c l i n i c a l l y c o n t r i b u t i n g t o i n s t r u m e n t b r e a k a g e
a n d c a n a l t r a n s p o r t a t i o n . T h e s e a r e a s s h o u l d b e s t u d i e d m o r e
t h o r o u g h l y , a n d t h e c l i n i c al e f f e c t o f r ad i u s o f c u r v a t u r e o n i n s t r u -
m e n t b r e a k a g e a n d r o o t c a n a l p r e p a r a t i o n s h a p e s h o u l d b e m o r e
c l e a r l y d e f i n e d .
T h e 3 0 - d e g r e e a n g l e g r o u p s h a d s i g n i f i c a n t l y g r e a t e r c y c l e s t o
f a i l u r e t h an t h e 4 5 - a n d 6 0 - d e g r e e a n g l e g r o u p s , r e g a r d l e s s o f s iz e
( F i g . 6 ) . T h i s w a s a n u n e x p e c t e d r e s u l t w h e n t h e e n g i n e e r i n g
l i t e r a t u r e w a s r e v i e w e d , w h e r e i n t h e e f f e c t o f a n g l e a l o n e
s e e m s
n e g l i g i b l e o r u n c e r t ai n . I t w a s s u s p e c t e d t h a t t h e 0 .8 3 m m d i a m e t e r
s t a i n l e s s - s t e e l t u b e s u s e d i n t h i s s t u d y , a l t h o u g h a l l o w i n g f r e e
r o t a t i o n o f t h e i n s t r u m e n t s , d i d n o t s u f f i c i e n t l y c o n s t r a i n t h e i n -
s t r u m e n t s h a f t s i n th e 3 0 - d e g r e e a n g l e g r o u p s . T h i s l a c k o f c o n -
s t r a i n t , a l t h o u g h n o t a f f e c t i n g t h e o v e r a l l a n g l e , d i d s l i g h t l y i n -
c r e a s e t h e e f f e c t i v e r ad i u s o f c u r v a t u r e , a l l o w i n g t h e i n s t r u m e n t
s h a f t t o f o l l o w a l a r g e r r a d iu s p a t h w i t h i n t h e g u i d e t u b e . D e p e n d -
i n g o n t h e a n g l e o f th e t u b e a n d t h e i n s t r u m e n t s h a f t d i a m e t e r , t h e
i n f l u e n c e o f a n g l e o f c u r v a t u r e w a s g e n e r a l l y c o n s i s t e n t i n b o t h t h e
2 - a n d 5 - r a m g r o u p s . H o w e v e r , i n t h e m o s t h i g h l y s t r e s s e d s t a t e s
s t u d i e d ( s iz e 4 0 i n s t r u m e n t s i n t h e 2 - r a m r a d i u s ) , i n c r e a s i n g a n g l e
r e s u l t e d i n a s i g n i f i c a n t d e c r e a s e i n c y c l e s t o f a i l u r e b e t w e e n a l l
t h r e e a n g l e g r o u p s . F u t u r e s t u d i e s s h o u l d a d d r e s s t h i s p o t e n t i a l
v a r i a b l e , m o r e p r e c i s e l y c o n t r o l l i n g i n s t r u m e n t c o n s t r a i n t t h r o u g h -
o u t t h e d e f i n e d c u r v a t u r e .
T h e L i g h t s p e e d i n s t r u m e n t i s o n e o f s e v e r a l N i - T i s y s t e m s
a v a i l a b l e t o t h e p r a c t i t i o n e r . T h e s e i n s t r u m e n t s h a v e a s m a l l c u t -
t i n g h e a d , w i t h a n o n c u t t i n g p i l o t t i p . T h e s h a f t o f t h e i n s t r u m e n t
i s
s m o o t h , n o n c u t t i n g , a n d h a s a d i a m e t e r t h a t i s s m a l l e r t h a n t h e
h e a d . T h e s e f e a t u r e s m a k e L i g h t s p e e d i n s t r u m e n t s g o o d e x p e r i -
m e n t a l i n s t r u m e n t s i n s e v e r a l re s p e c t s . I n p a r ti c u l a r , t h e d e s i g n o f
t h e a p p a r a tu s u s e d f o r c y c l i c f a t ig u e t e s t i n g c o u l d b e s i m p l i f i e d ,
a l l o w i n g t h e a p p a r a t u s t o c r e a t e t e s t s t r e s s e s s i m i l a r t o t y p i c a l
C yc l i c F a t i g u e o f N i - T i R o t a ry I n s t ru m en t s 83
f a t ig u e - t es t e q u i p m e n t c o m m o n l y u s e d i n o t h e r m e t a l l u r g i c a p p l i -
c a t i o n s . T h e s l e n d e r s h a f t a l lo w s q u i t e s e v e r e b e n d s w i t h o u t p e r -
m a n e n t d e f o r m a t i o n , t h u s l e n d i n g i t s e l f t o a w i d e r r a n g e o f c u r -
v a t u r e c o n d i t i o n s . A p r e d i c t a b l e m e t a l s h a f t d i a m e t e r e l i m i n a t e d
h a v i n g t o a c c o u n t f o r a d d i t i o n a l v a r i a b l e s , s u c h a s i n s t r u m e n t
f l u t e s an d t a p e r . T h e s e c h a r a c t e r i s ti c s , h o w e v e r , d o n o t p r e v e n t t h e
s e p a r a t i o n o f L i g h t s p e e d i n s t r u m e n t s . A l l i n s t ru m e n t s t e s t e d i n th i s
s t u d y s e p a r a t e d w i t h i n a 5 - m i n t i m e l i m i t .
A n o t h e r a d v a n t a g e o f u s i n g t h e L i g h t s p e e d i n s t r u m e n t i n th i s
s t u d y w a s t h a t o p e r a t io n h a s b e e n a d v o c a t e d o v e r a w i d e r a n g e o f
s p e e d s . T o i n v e s t i g a t e t h e e f f e c t o f r p m o n c y c l i c f a t i g u e , t e s t in g
w a s p e r f o r m e d a t 7 5 0 , 1 3 0 0 , a n d 2 0 0 0 r p m . T h e t h r e e r p m g r o u p s
w e r e n o t s t a t i s t i c a l l y d i f f e r e n t f r o m o n e a n o t h e r ( F i g . 4 ) . U p o n
r o t a t io n , r i s i n g s t r es s l e v e l s c a u s e m o v e m e n t o f d i s l o c a t i o n d e f e c t s
a n d b r e a k s a t o m i c b o n d s w i t h i n t h e c r y s t a l l i n e m a t r i x o f t h e a l l o y ,
l e a d i n g t o c r a c k i n i t ia t i o n a n d p r o p a g a t i o n . T h e s h a r p n e s s o f t h e
c r a c k t i p c a u s e s e x t r e m e s t r e s s c o n c e n t r a t i o n e x c e e d i n g t h e
s t r e n g t h o f t h e m e t a l a t t h e c r a c k t i p i n t e n s i o n . T h e f r a c t u r e
p r o p a g a t e s a s h o r t d i s t a n c e u n d e r t e n s i o n , t h e n d u c t i l e d e f o r m a t i o n
b l u n t s t h e c r a c k t i p , s t o p p i n g t h e p r o p a g a t i o n . I n t h e o t h e r h a l f o f
t h e c y c l e , u n d e r c o m p r e s s i o n , t h e a l l o y b u c k l e s m i c r o s c o p i c a l l y
a n d t h e c r a c k r e s h a r p e n s ( 9 ) . T h i s m i n u t e p r o p a g a t i o n o c c u r s o n
t h e o r d e r o f 1 0 - 6 s o r a p p r o x i m a t e l y a t t h e s p e ed o f s o u n d i n m e t a l
( l 7 ) , a n d t h e p r o p a g a t i o n e v e n t i s c o m p l e t e d m u c h f a s t e r th a n t h e
i n s t r u m e n t i s r o t at i n g . T h u s , c y c l i c f a ti g u e a n d t h e u l t i m a t e n u m b e r
o f c y c l e s t o f a i l u r e ar e u n a f f e c t e d b y t h e r p m .
I t i s i m p o r t a n t t o r e c o g n i z e t h a t a n i n s t r u m e n t h a s a m e a n
n u m b e r o f c y c l e s t o f a i l u r e t h a t is d e t e r m i n e d b y s p e c i f i c p a r a m -
e t e r s o f c a n a l ra d i u s , c a n a l a n g l e , a n d i n s t r u m e n t d i a m e t e r . A
h i g h e r r p m w i l l c o n s u m e t h e u s e f u l l i f e o f t h e i n s t r u m e n t m u c h
f a s t e r t h a n a l o w e r r p m . T h u s , a l o w e r r p m w o u l d b e b e n e f i c i a l a n d
p r o v i d e a g r e a t e r c li n i c a l li f e , m o r e s l o w l y u s i n g t h e f i n i t e n u m b e r
o f c y c l e s t o f a i l u r e a v a i la b l e . T h i s i s e s p e c i a l l y t r u e w h e n a N i - T i
r o t a r y i n s t r u m e n t i s u s e d i n s e v e r e c u r v a t u r e c o n d i t i o n s s u s p e c t e d
t o i n d u c e s t re s s f a ti g u e . A l t h o u g h a w i d e r a n g e o f o p e r a t i n g s p e e d s
h a s b e e n a d v o c a t e d f o r N i - T i , e n g i n e - d r i v e n s y s t e m s , t h o s e r e c -
o m m e n d a t i o n s m u s t t a k e i n t o a c c o u n t m o r e t h a n j u s t c y c l i c f a t i g u e
a s a c au s e o f i n s t r u m e n t s e p a r a t io n . N o n e t h e l e s s , t h e e f f e c t o f r p m
w h e n s t u d y i n g t h e b r e a k a g e o f N i - T i i n s t r u m e n t s h a s n o t b e e n
p r e v i o u s l y e x a m i n e d a n d , i n t h e p r e s e n t t e s t c o n d i t i o n s , r p m h a d n o
e f f e c t o n c y c l e s t o f a i l u r e .
T h e r e s u l t s o f o u r i n v e s t i g a t i o n c o n f i r m e d t h a t i n s t r u m e n t l i f e
s p a n i s i n v e r s e l y p r o p o r t i o n a l t o i n s t r u m e n t s i z e 0 2 , 1 3 ) an d t h a t
m e t a l f a t i g u e i s d e e p l y i m p l i c a t e d i n f i l e b r e a k a g e ( 2 , 8 ). L a r g e r
d i a m e t e r i n s t r u m e n t s h a d a l o w e r f a t i g u e l i f e , r e s u l t i n g i n s i g n i f -
i c a n t l y f e w e r c y c l e s t o f a i l u r e t h a n s m a l l e r d i a m e t e r i n s t r u m e n t s
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t w o i n s t r u m e n t s i s o n l y 0 . 0 4 6 r a m . T h e l a r g e r d i a m e t e r i n s t r u m e n t
w a s u n d e r m o r e s t r e ss w i t h i n t h e c o n f i n e s o f a d e f i n e d c u r v a t u r e .
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f a i l u r e , la r g e r i n s t ru m e n t s s h o u l d n o t b e c o n s i d e r e d s a f e r o r s t r o n -
g e r i n c l i n i c a l p r a ct i c e . I n f a ct , r o t a r y N i - T i i n s t r u m e n t s w i t h l a r g e r
d i a m e t e r s w o u l d b e e x p e c t e d t o s e p a r a t e a t f e w e r c y c l e s t h a n
s m a l l e r d i a m e t e r i n s t r u m e n t s .
T h e r e s u l t s o f o u r s t u d y s h o u l d n o t b e i n t e r p r e t e d a s a f i x e d
m e a n n u m b e r o f c y c l e s to f a i l u r e f o r e i t h e r s i z e 3 0 o r 4 0
L i g h t s p e e d i n s t r u m e n t d u r i n g c l i n i c a l u s e . T w o i m p o r t a n t p o i n t s o f
e x p l a n a t i o n a r e re q u i r e d . F i r s t , th e p o i n t o f m a x i m a l f l e x u r e i n t h e
c u r v a t u r e a n d , t h e r e f o r e , t h e s t r e s s o n t h e i n s t r u m e n t d u r i n g t h i s
s t u d y w a s i n a c o n s t a n t f i x e d l o c a t i o n u n t i l s e p a r a t i o n o c c u r r e d .
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8/10/2019 cyclic fatigue of NiTi instruments
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p e c t e d , a s c o n c l u d e d b y D e d e r i c h e t a t . ( 1 2 ) e x a m i n i n g s t a i n l e s s -
s t e e l i n s t r u m e n t s , to s i g n i f i c a n t l y e x t e n d i n s t r u m e n t l if e . N i - T i
i n s t r u m e n t m a n u f a c t u r e r s s u g g e s t t h a t th e s e i n s t r u m e n t s b e u s e d
w i t h c o n t i n u o u s a x i a l m o t i o n i n t h e c a n a l . L i n g e r i n g a t a s i n g l e
d e p t h i n t h e c a n a l w o u l d c l o s e l y d u p l i c a t e t h e t e s t c o n d i t i o n s o f
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a t a s p e c i f i c p o i n t a l o n g t h e i n s t r u m e n t s h a ft . T h i s m o d e o f o p e r -
a t i o n i s d i s c o u r a g e d a n d s h o u l d b e a v o i d e d .
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e x t e n s i v e l y i n v e s t i g a t e d ( 1 8 - 2 0 ) , a n d t h e f a t i g u e b e h a v i o r o f N i - T i
a l l o y s h a s b e e n s h o w n t o b e r e l a t e d t o t h e s t a t i c y i e l d s t r es s o f t h e
a l l o y . A t l o w s t a ti c s t r e ss , t h e a l l o y e x h i b i t s l i n e a r s t r ai n . O n c e t h e
s t r e ss r i s e s a b o v e t h e y i e l d s t r e s s , s m a l l i n c r e a s e s i n t h e s t re s s w i l l
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r e v e r s i b l e . T h i s i s t h e s o - c a l l e d s u p e r e l a s t i c c h a r a c t e r i s t i c . N i - T i
f a t i g u e t e s ts c o n d u c t e d b e l o w t h e y i e l d s t r e s s g i v e r e s u l t s s i m i l a r to
f e r r o u s a l l o y s , s u c h a s s t a i n l e s s s t e e l . F a t i g u e t e s t s c o n d u c t e d
a b o v e t h e y i e l d s t r es s i n t h e s u p e r e l a s t i c r a n g e g i v e s r i s e t o d i s t i n c t
l o w - c y c l e f a t i g u e b e h a v i o r ( 1 8 ) , w h i c h r e s u l t s i n v e r y r a p i d r e d u c -
t i o n s i n f a t i g u e l i f e w i t h i n c r e a s i n g s t r e s s. T h i s l o w - c y c l e f a t i g u e
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o r f l e x u r e o f t h e s p e c i m e n t h a n t o t h e s t r e ss l e v e l a n d i s l a rg e l y a
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w i t h g r e a t e r f l e x u r e s h a v i n g a s h o r t e r e x p e c t e d l i f e . T h e p i l o t
s t u d i e s u s e d t o d e t e r m i n e t h e t e s t p a r a m e t e r s s u g g e s t e d t h a t t h e
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d e g r e e s , l o w - c y c l e f a t i g u e b e h a v i o r r e s u l t e d . A t 2 5 d e g r e e s a n d
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h e l p s e x p l a i n t h e s i g n i f i c a n t d i f f e r e n c e s i n t h e t e s t g r o u p s w h e n
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i n c r e a s i n g t h e a n g l e o f c u r v a t u r e ; b o t h r e s u l t e d i n i n c r e a s e d s t r a in .
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c a n a l c u r v a t u r e d e t e r m i n e ~ t r a d i o g r a p h i c a l l y . F l e x e d c o n d i t i o n s
r e s u l t i n g i n c h a r a c t e r i s t i c s o f r e l a t i v e l y l o w s t a i n a n d e l a s t i c d e -
f o r m a t i o n w o u l d b e e x p e c t e d t o e x h i b i t i n c r e a s e d n u m b e r o f c y c l e s
t o f a i l u r e s e v e r a l o r d er s o f m a g n i t u d e h i g h e r t h a n t h o s e d e t e r m i n e d
in th is s tudy (18) .
A l l i n s t r u m e n t s t e s t e d s e p a r a t e d a t t h e p o i n t o f m a x i m u m f l e x -
u r e w i t h i n th e c u r v e d s e g m e n t o f t h e tu b e , w h e r e i n t h e s t r e s s o n t h e
i n s t r u m e n t w a s g r e a te s t ( F i g . 8 ). T h e f r a c t u r e d s u r f a c e s s e e m e d
s i m i l a r t o t h o s e p r e v i o u s l y o b s e r v e d f o r f a t i g u e t e s t i n g ( 1 i ) . U n -
f l e x e d , p a r t i a ll y f r a c t u r e d N i - T i i n s t r u m e n t s s e e m e d n o r m a l w i t h -
o u t p e r m a n e n t p l a st i c d e f o r m a t i o n. U n d e r f l e x u re , o p e n i n g o f t h e
f r a c t u r e s w a s e v i d e n t a n d g e n e r a l l y s e e m e d t o b e a s s o c i a t e d w i t h
f l a w s o n t h e i n s t r u m e n t s ur f a ce d i r e c t ly i n t h e a r e a o f m a x i m u m
f l e x u r e . N o i n s t r u m e n t s p e c i m e n s e p a r a t e d a t o r j u s t b e h i n d t h e
h e a d o f t h e i n s t r u m e n t i n a s u c c e s s f u l t e s t t o i ts c y c l i c f a t i g u e l i m i t .
T h i s c o n t r a d i c t s r e p o r t s s u g g e s t i n g t h a t t h e C a n a l M a s t e r i n s t r u -
m e n t d e s i g n i s p r o n e t o s e p a r a t i o n j u s t b e h i n d t h e h e a d o r i n t h e
a p i c a l t h i rd . S t a t i c t o r s i o n a l s t u d ie s h a v e s h o w n t h a t s e p a r a t i o n o f
J o u r n a l o f E n d o d o n t i c s
N i - T i L i g h t s p e e d i n s t r u m e n t s a l w a y s o c c u r re d - - 2 m m b e h i n d t h e
i n s t r u m e n t h e a d ( 7 ) . T h a t f a i l u r e m o d e i s l i m i t e d t o s t a t i c t e s ti n g .
I f i n s t r u m e n t s e p a r a ti o n o c c u r s b e h i n d t h e h e a d o f t h e i n s t r u m e n t
c l i n i c a l l y , tw o e x p l a n a t i o n s a r e p o s s i b l e . F i r st , s e p a r a t i o n o c c u r r e d
a s t h e r e s u l t o f l o c k i n g o r t o r s i o n a l o v e r l o a d i n g o f t h e i n s t r u m e n t
h e a d d u r i n g r o t a t i o n . S e c o n d , s t r e s s i n a c u r v e d c a n a l c a n c a u s e
f a t i g u e f a i l u r e d i r e c tl y b e h i n d t h e h e a d . T h e h e a d i s i n f l e x i b l e a n d
m u s t p a s s t h r o u g h a n y c u r v a t u r e t h a t t h e s h a f t e x p e r i e n c e s . E x -
c e s s i v e a p i c a l l y d i r e c t e d f o r c e o n t h e i n s t r u m e n t w i l t c a u s e t h e
s h a f t t o f le x j u s t b e h i n d t h e h e a d . B o t h c i r c u m s t a n c e s l e a d t o s t r e s s
c o n c e n t r a t i o n c a u s i n g f a t i g u e d a m a g e , a c c e l e r a t i n g s e p a r a t i o n
c a u s e d b y b i n d i n g a n d f a t i g u e. S e p a r a t io n o f u n b o u n d i n s t r u m e n t s
i n t h e a r e a o f t h e m o s t s e v e r e c a n a l c u r v a t u r e s h o u l d a l w a y s b e
c o n s i d e r e d a r e s u l t o f c y c l i c f a t i g u e w i t h a n y i n s t r u m e n t s y s t e m .
F u r t h e r s t u d y i s r e q u i r e d t o i m p r o v e t h e u n d e r s t a n d i n g o f c r i -
t e r i a t h a t m a y b e u s e d t o p r e d i c t N i - T i i n s t r u m e n t fa t i g u e l e a d i n g
t o s e p a r a ti o n . T h e f a t ig u e o f a n i n s t r u m e n t c a n b e b r o k e n d o w n
i n t o s t a g es a s e v i d e n t o n S E M e x a m i n a t i o n ( F i g . 9 ) . S t a g e I , c r a c k
i n i t i a t i o n , i s c h a r a c t e r iz e d b y t h e s m o o t h , a l m o s t f e a t u r e l e s s a r e a a t
t h e s u r f a c e p e r i p h e r y . T h i s a r e a o f f r a c t u re i n i t i a t i o n m a y b e r e -
v e r s i b l e t h r o u g h p r o p e r h e a t t r e a t m e n t ( 9 ) . S t e r i l iz a t i o n h a s b e e n
s u g g e s t e d t o e n h a n c e t h e f a t i g u e l i fe o f N i - T i f i l e s a n d r e v e r s e t h e
s t r e s s - i n d u c e d m a r t e n s i t e t r a n s f o r m a t i o n t o t h e p a r e n t a u s t e n i t e
p h a s e ( 2 ) . F u r t h e r m o r e , s t e r i l i z a t i o n m a y r e v e r s e t h e c r a c k i n i t i a -
t i o n s t a g e o f f r a c t u r e i n N i - T i a l l o y s , b u t t h i s i s a n a r e a f o r f u t u r e
i n v e s t i g a t i o n . T o r s i o n a l l o a d i n g d u r i n g r o t a t i o n a l u s e i s a n o t h e r
v a r i a b l e t o c o n s i d e r t h a t m a y d r a m a t i c a l l y i n f l u e n c e th e c y c l i c
f a t i g u e l i f e o f i n s t r u m e n t s . E n g a g e d i n s t r u m e n t s th a t a r e a c t i v e l y
c u t t i n g d e n t i n w o u l d b e e x p e c t e d t o h a v e d i f f e r e n t f a t i g u e c h a r a c -
t e ri s ti c s. T h e c y c l i c f a ti g u e p h e n o m e n o n m a y b e f u r t h e r c o m -
p o u n d e d b y t h e a d d i t i o n o f f l u t e s t o t h e s h a f t a n d b y i n s t r u m e n t
t a p e r . F l u t e s c o u l d a c t a s s t r e s s c o n c e n t r a t o r s o n t h e i n s t r u m e n t
s h a f t, p o t e n t i a l l y r e s u l t i n g i n m o r e r a p i d c r a c k i n i t i a t i o n . I n s t r u -
m e n t t a p e r e n l a r g e s t h e d i a m e t e r o f t he i n s t r u m e n t i n t h e a r e a o f a
c o r o n a l c u r v a t u r e , c o m p a r e d w i t h t h e a p i c a l a r e a, t h u s r e s u l t i n g i n
h i g h e r s t r e s s c a u s e d b y a l a r g e r c r o s s - s e c t i o n a l d i a m e t e r . T h e
e f f e c t o f i n s t r u m e n t f l u te s a n d c r o s s - s e c t i o n a l d i a m e t e r s i s a n a r e a
o f c o n c e r n , p a r t i c u l a r ly w i t h t h e i n t r o d u c t i on o f n o n s t a n d a r d i z e d
t a p e r e d N i - T i i n s t r u m e n t s . T h e s e a r e a s s h o u l d b e a d d r e s s e d i n t h e
d e s i g n o f N i - T i , e n g i n e - d r i v e n ro t ar y i n s t r u m e n t s a n d w a r r a n t
fu r the r s tudy .
S p e c i f ic r e c o m m e n d a t i o n s f o r p r e v e n t i n g b r e a k a g e o f L i g h t -
s p e e d i n s t r u m e n t s c a n n o t b e d r a w n f r o m t h i s s tu d y . H o w e v e r ,
b e c a u s e p a r t i a l l y f a t i g u e d i n s t r u m e n t s d i d n o t d e m o n s t r a t e v i s i b l e
d e f o r m a t i o n , y e t d i d e x h i b i t c r a c k fo r m a t i o n , a g e n e r a l c o n c l u s i o n
c a n b e m a d e . T o p r e v e n t t h e b r e a k a g e o f N i - T i , e n g i n e - d r i v e n
i n s t r u m e n t s s e c o n d a r y t o c y c l i c f a t i g u e , i t s e e m s t h a t t h e b e s t
r e c o m m e n d a t i o n i s t o d i s c a r d t h e m a f t e r a s p e c i f i e d u s e p e r i o d a s
r e c o m m e n d e d f o r s t a i n l e s s - s t e e l i n s t r u m e n t s . T h a t u s e p e r i o d
w o u l d b e e x p e c t ed t o v a r y w i d e l y d e p e n d i n g o n i n s t r u m e n t d e s ig n ,
s i z e , a n d s t re s s e s p l a c e d o n i t b e c a u s e o f th e m a n n e r o f u s e, a n d t h e
c a n a l c u r v a t u r e p r e p a r e d . I n s o m e s e v e r e a n g l e s h a v i n g a s m a l l
r a d i u s o f c u r v a t u r e a n d a l a r g e a n g l e o f c u r v a t u r e , d i s c a r d i n g a n
i n s t r u m e n t a ft e r a s i n g l e u s e m a y b e t h e s a f e s t a d v i c e .
C a n a l c u r v a t u r e a n d a n g l e h a v e b e e n i m p l i c a t ed i n i n s t r u m e n t
s e p a r a t i o n . C y c l i c m e t a l f a t i g u e h a s b e e n f u r t h e r i m p l i c a t e d , a s a n
i m p o r t a n t f a c to r i n i n s t r u m e n t b r e a k a g e . T h i s s t u d y c l e a r l y s h o w e d
t h a t , i n c y c l i c f a t i g u e t e s t i n g , c y c l e s t o f a i l u r e i s i n v e r s e l y p r o p o r -
t i o n a l t o i n s t r u m e n t st r e ss . S m a l l e r r a d i u s o f c u r v a t u r e a n d i n -
c r e a s e d i n s t r u m e n t d i a m e t e r r e su l t e d i n f e w e r c y c l e s t o f a i l u r e
c a u s e d b y h i g h e r i n s t r u m e n t st r es s . C y c l e s t o f a il u r e w a s n o t
a f f e c t e d b y o p e r a t i n g r p m , a n d t h e e f f e c t o f a n g l e a l o n e o n c y c l e s
8/10/2019 cyclic fatigue of NiTi instruments
9/9
V o l. 2 3 N o . 2 F e b r u a r y 1 9 9 7
t o f a i lu r e w a s u n c l e a r . N e w N i - T i i n s t r u m e n t s y s t e m s a r e c u r r e n t l y
b e i n g r e c o m m e n d e d f o r u s e i n a c o n t i n u o u s l y r o t a r y m a n n e r a n d
a g r o w i n g n u m b e r o f in c i d e n t s o f in s t r u m e n t s e p a r a t io n a r e b e i n g
i n f o r m a l l y d i s c u s s e d . G i v e n t h e i n c r e a s e d n u m b e r o f N i - T i e n d -
o d o n t i c i n s t r u m e n t s y s t e m s o n th e m a r k e t t h e s e p r o b l e m s a r e
l i k e l y t o b e c o m e m o r e c o m m o n . T o d a t e t h e r e is n o te s t p r o t o c o l
t h a t s e t s m i n i m u m s t a n d a r d s f o r c y c l i c f a t i g u e o f t h e s e i n s t r u -
m e n t s n o r a r e t h e o p e r a t i n g p a r a m e t e r s o f i m p o r t a n c e y e t f u l l y
u n d e r s t o o d . T h i s s t u d y c o n c l u d e s w i t h a c a ll f o r a c o m p r e h e n s i v e
c y c l i c f a t i g u e t e s t s p e c i f i c a t i o n f o r a l l r o t a r y e n d o d o n t i c i n s t r u -
m e n t s i n c l u d i n g N i - T i i n s t r u m e n t s d e s i g n e d t o b e e n g i n e - d r i v e n
a n d f u l l y p r e p a r e c u r v e d c a n a ls . F u r t h e r m o r e t h e p a r a m e t e r s o f
a n g l e o f c u r v a t u r e a n d r a d i u s o f c u r v a t u r e a n d i n s t r u m e n t c r o s s -
s e c t i o n a l c o r e d i a m e t e r m u s t b e i n c l u d e d i n a n y s u c h s p e c i f i c a t i o n .
W i t h o u t i n v e s t i g a t i o n o f t h e s e p a r a m e t e r s r e c o m m e n d a t i o n s f o r
t h e s a fe u s e o f N i - T i e n g i n e - d r i v e n r o t a ry i n s t r u m e n t s w i l l r e m a i n
s p e c u l a t i v e . T h e r e s u l t s a l s o s u g g e s t t h a t t h e e f f e c t o f t h e r a d i u s o f
c u r v a t u r e a s a n i n d e p e n d e n t v a r i a b l e s h o u l d b e c o n s i d e r e d i n
s t u d i e s e v a l u a t i n g r o o t c a n a l i n s t r u m e n t a t i o n .
Th is s t u d y w a s su p p o r t e d i n p a r t b y a n E n d o d o n t i c S t u d e n t A w a rd f r o m
the Research and Educat ion Foundat ion o f the Amer i can Associa t i on o f
Endodont i s ts .
The op in ions, asse r t i ons, mater ia l s, and m ethodo log ies here in a re p r i va te
ones o f the au thors and are no t to be c onst rued as o f f i c ia l o r re f lect ing the
v i e w s o f t h e A m e r i ca n A sso c i a t io n o f E n d o d o n t i s ts o r t h e Fo u n d a t io n .
We gra te fu l l y acknow ledge David S . P i t tman o f Sunset Resources, Inc.
San Anton io , TX) fo r mod i fy ing and wr i t i ng the da ta co l l ect i on p rog ram fo r the
Magt ro l Dynamometer . We express our g ra t i tude to Drs. James A . Gi l l es,
Wi l l iam A. Walker I l l , and Carlos E. del Rio for thei r advice during art icle
prepara t ion .
Drs. P rue t t , C lement , and Carnes are a f f i l i a ted w i th the Depar tment o f
Endodo nt i cs/Denta l Schoo l , Un ivers ity o f Texas Hea l th S cience Center a t San
Anton io , San Anton io , TX . Address requests fo r repr in ts to Dr . David L .
Carnes, Jr . , Depar tment o f Endodont i cs/Denta l Schoo l , Un ivers i ty o f Texas
Hea l th Science Center a t San Anton io , 7703 F loyd Cur l Dr ive , San Anton io , iX
78284-7898.
C y c l i c F a t i g u e o f N i - T i R o t a r y I n s t r u m e n t s 8 5
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You Migh t e In te res ted
A case o f f raud was recen t ly uncovered in wh ich an imposte r had , over the past 25 years , managed to ge t
a number o f essays and le t te rs to the ed i to r pub l ished in respected journa ls . The JAM A unm asked the rasca l
because h is wr i t ing s ty le had been recogn ized (BMJ 311 523 , 1995) .
Of course , there was ano ther c lue . The f ic t ic ious name s igned to a l l those pub l ished le t te rs over a l l those
ye a rs w a s - -yo u ' l l l o ve t h i s - -T . H . F id d lema n .
Zachariah eomans